STNB2018 (32nd edition)

Generalized Heegner cycles and p-adic L-functions

Francesca Gatti

Abstract

In this talk, we will introduce natural generalizations of the classical Heegner points, the so-called Heegner cycles. Such objects are classes in the isotypical component of cohomology of a modular or Shimura curve provided by a weight $2k$ modular form. These classes are obtained from diagonal cycles of the Kuga-Sato variety associated with complex multiplication elliptic curves. Moreover, we will explain Bertolini, Darmon and Prasanna result on generalized Heegner cycles that relates the Block-Kato logarithm of such classes with the value of a certain $p$-adic $L$-function.